{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 14: Fitting functions to data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Helper functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_function(f,xmin,xmax,**kwargs):\n",
    "    ts = np.linspace(xmin,xmax,1000)\n",
    "    plt.plot(ts,[f(t) for t in ts],**kwargs)\n",
    "    \n",
    "def scalar_field_heatmap(f,xmin,xmax,ymin,ymax,xsteps=100,ysteps=100):\n",
    "    fig = plt.figure()\n",
    "    fig.set_size_inches(7,7)\n",
    "    fv = np.vectorize(f)\n",
    "    X = np.linspace(xmin, xmax, xsteps)\n",
    "    Y = np.linspace(ymin, ymax, ysteps)\n",
    "    X, Y = np.meshgrid(X, Y)\n",
    "    z = fv(X,Y)\n",
    "    fig, ax = plt.subplots()\n",
    "    c = ax.pcolormesh(X,Y,z, cmap='plasma')\n",
    "    ax.axis([X.min(), X.max(), Y.min(), Y.max()])\n",
    "    fig.colorbar(c, ax=ax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from vectors import length \n",
    "def secant_slope(f,xmin,xmax):\n",
    "    return (f(xmax) - f(xmin)) / (xmax - xmin)\n",
    "\n",
    "def approx_derivative(f,x,dx=1e-6):\n",
    "    return secant_slope(f,x-dx,x+dx)\n",
    "\n",
    "def approx_gradient(f,x0,y0,dx=1e-6):\n",
    "    partial_x = approx_derivative(lambda x:f(x,y0),x0,dx=dx)\n",
    "    partial_y = approx_derivative(lambda y:f(x0,y),y0,dx=dx)\n",
    "    return (partial_x,partial_y)\n",
    "    \n",
    "def gradient_descent(f,xstart,ystart,tolerance=1e-6):\n",
    "    x = xstart\n",
    "    y = ystart\n",
    "    grad = approx_gradient(f,x,y)\n",
    "    while length(grad) > tolerance:\n",
    "        x -= 0.01 * grad[0]\n",
    "        y -= 0.01 * grad[1]\n",
    "        grad = approx_gradient(f,x,y)\n",
    "    return x,y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "import car data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from car_data import priuses"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 14.1 Measuring the quality of fit for a function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 14.1.1 Measuring distance from a function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_data = [\n",
    "     (-1.0, -2.0137862606487387),\n",
    "     (-0.9, -1.7730222478628337),\n",
    "     (-0.8, -1.5510125944820812),\n",
    "     (-0.7, -1.6071832453434687),\n",
    "     (-0.6, -0.7530149734137868),\n",
    "     (-0.5, -1.4185018340443283),\n",
    "     (-0.4, -0.6055579756271128),\n",
    "     (-0.3, -1.0067254915961406),\n",
    "     (-0.2, -0.4382360549665138),\n",
    "     (-0.1, -0.17621952751051906),\n",
    "     (0.0, -0.12218090884626329),\n",
    "     (0.1, 0.07428573423209717),\n",
    "     (0.2, 0.4268795998864943),\n",
    "     (0.3, 0.7254661223608084),\n",
    "     (0.4, 0.04798697977420063),\n",
    "     (0.5, 1.1578103735448106),\n",
    "     (0.6, 1.5684111061340824),\n",
    "     (0.7, 1.157745051031345),\n",
    "     (0.8, 2.1744401978240675),\n",
    "     (0.9, 1.6380001974121732),\n",
    "     (1.0, 2.538951262545233)\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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2bRsNGjSgdevW3H777SxdupRFixYpxMUjFOQiOXDixAn+/ve/8+ijj/Lzzz/zySefEBUVxe+lKlN/1AoeDllM/VErWBAV6+lSJR9Ra0UkGy5fvsyHH37I8OHDuXz5Mr1792bgwIGUKFHiD5eijY1LoP/8nYB3n+iT3nXQvbleyZiOyEUyYa3l66+/pnLlyoSEhNCgQQN27dpFREQEJUqUAG68FG2qhGtJjFkS7YmSsyX1wyc2LgHL/3/46C8J3+SUIDfGNDXGRBtj9htjQpyxThFPi4qK4tlnn6VNmzYUK1aMZcuWsWDBAgICAm543LG4hHSfn9Fyb+CLHz6SsVwHuTGmIDABeAGoDHQwxlTO7XpFPOW3336jW7duPPbYY+zevZuJEycSFRVFw4YN0318mQwuOZvRcm/gix8+kjFnHJE/Duy31h601l4F5gAtnbBeEbe6fPkyI0eOJCAggC+++II+ffqwf//+Gy5ulZ5+TSrgV6jgDcu8/VK0vvjhIxlzRpD7A0fS/H7UsewGxpjuxpjNxpjNp06dcsJmRZzDWstXX31FpUqVGDBgAI0aNWL37t2MGTOGu+66K8vnt6rlz8jW1fAv4eczl6L1xQ8fyZjbRq1YaycDkwECAwOtu7YrkpktW7YQFBTEmjVrqF69OsuXL6dBgwY5Xk+rWv5eHdw3S61Vo1byBmcEeSzwQJrfyzqWiXit48ePExoayvTp0ylVqhSTJ0/mjTfeoGDBglk/OY/wtQ8fyZgzWiubgABjzMPGmMJAe2CRE9Yr4nQJCQmMGDGCgIAAZs2aRb9+/YiJiaF0YDOeHrNKJ/SIT8r1Ebm1NtEY0xNYAhQEPrPW7sp1ZSJOZK1l3rx5vPfeexw+fJjWrVszevRo/vKXv/jsCT0iqZzSI7fWRgKRzliXyK3K6EzFzZs3ExQUxNq1a6lRowbTpk3jueeeu/68zMZUK8jFF+jMTskT0jtTse+MlTRo0ZbatWuzb98+pkyZwpYtW24IcdCYavF9utaK5Alpj6qTr13h4qYFnN8wj4PJSQQHBzNgwADuvPPOdJ9bpoQfsemEtsZUi69QkEuecCwuAWstl/au4dzKaSRdOMXt5etR8rk3GDWqW6bP7dekwg09ctCYavEtCnLJE4pfPMy+hR9xJXYPhe75M6Ve7E3RB1NO0smKxlSLr1OQi0+LjY1lwIAB7Pz8cwoWK8ndL7xLsaoNMQUK5uioWmOqxZcpyMUnXbp0ibFjxzJq1CgSExMJCQmh+otd+WhtrI6qJd9RkItPsdYyZ84cgoODOXLkCG3atGH06NE8/PDDAHR4Un1tyX80/FB8xn//+1/q169Px44dKV26NKtWrWLevHnXQ1wkv1KQi9c7evQonTt3pk6dOhw6dIjPPvuMTZs28fTTT3u6NBGvoNaKeK1Lly4RERFBeHg4SUlJDBgwgJCQEIoXL+7p0kS8ioJcvI61ltmzZxMcHMzRo0dp27Yt4eHhlCtXztOliXgltVbEq4TPWMSdD1WhU6dOnLO3M/zT+cydO1chLpIJBbl4hSNHjvBMs9aEdG1JwrkT3N0siLs7RfDFIT9dUlYkC2qtiEf9/vvvjBkzhtGjR3P5WiJ3PtGOu+q2oUDhlDMydRVCkawpyMUjkpOT+fe//01ISAixsbG0a9eOdSWbUPCue/7wWF2FUCRzaq2I223YsIF69erx+uuvc//997N27VrmzJnDgw89lO7jdRVCkcwpyMVtjhw5QqdOnXjiiSf49ddfmTFjBhs3bqR+/fqAZnYXuVVqrYjL/f7774wePZoxY8ZgreV///d/ee+997jjjjtueJyuQihyaxTk8gcZTZmWU8nJycyaNYuQkBCOHTtGhw4dGDVqFA8++GCGz9FVCEVyTkEuN3DWRMTr16+nV69ebNq0idq1azNv3jzq1avnkppF8jv1yOUGmU1EnB2HDx+mQ4cO1K9fn2PHjvHFF19c/3JTRFxDR+Ryg1udiDg+Pp7w8HAiIiIwxjB48GD69etHsWLFXFGmiKShIJcb5HQi4uTkZL744gv69+/P8ePH6dixI6NGjeKBBx5wdaki4qDWitwgJ0MA161bR506dejatSsPPvgg69evZ9asWQpxETfTEbkXc9bokZzIzhDAw4cPExwczNy5c/H392fmzJl06NCBAgV0XCDiCQpyL+Ws0SO3IqMhgPHx8YwaNYqIiAgKFCjAkCFD6Nu3r/rgIh6mQygvldvRI86UnJzM9OnTCQgIYPjw4bz66qvs27ePwYMHK8RFvICOyL3UrY4ecbY1a9YQFBTEli1bqFu3LgsWLKBOnTpurUFEMqcjci+V0SgRd11A6tChQ7Rt25ann36aEydOMGvWLNavX68QF/FCCnIv5akLSF28eJEBAwZQqVIlFi9eTFhYGNHR0XTs2BFjjEu3LSK3Rq0VL+XuC0glJyczY8YMBgwYwG+//cbrr7/OiBEjKFu2rEu2JyLOoyD3Yu66gNTq1avp1asXUVFRPPHEEyxcuJDHH3/c5dsVEedQayUfO3ToEK+++irPPPMMp0+fZvbs2axbt04hLuJjFOT50IULF+jfvz8VK1YkMjKSoUOHEh0dTfv27dUHF/FBaq3kI0lJSUyfPp3Q0FBOnDhBly5dGD58OP7+uv63iC/LVZAbY14FhgCVgMettZudUZQ436pVq+jVqxfbtm2jfv36fPvtt9SuXdsl2/LEpQVE8rPctlZ+BloDq51Qi7jAwYMHeeWVV3j22Wc5e/Ysc+bMYc2aNS4N8f7zdxIbl4Dl/y8tsCAq1iXbE5FcBrm1do+11v3njEuWLly4QHBwMJUqVWLJkiUMGzaMvXv30q5dO5f2wb3p0gIi+YXbeuTGmO5AdyDTORsld5KSkpg2bRqhoaGcPHmSrl27Mnz4cMqUKeOW7XvLpQVE8pMsg9wYswy4L527Qq21C7O7IWvtZGAyQGBgoM12hZJtP/30E0FBQWzfvp0nn3ySxYsXExgY6NYacjoxhYjkXpatFWttI2tt1XR+sh3i4loHDhygdevWNGjQgLi4OL788ktWr17t9hAHz11aQCQ/0/BDH3b+/HmGDx/Ohx9+SKFChRgxYgRBQUEULVrUYzW5+9ICIpL74YcvA+OB0sBiY8w2a20Tp1QmGUpKSuLTTz9l4MCBnD59mr/+9a8MGzaM+++/39OlAe67tICIpMhVkFtrvwG+cVItkg0rVqwgKCiIHTt28NRTT/HBBx/w6KOPerosEfEgnaLvI2JiYmjVqhUNGzbkwoULzJs3j1WrVinERURB7u3i4uLo27cvVapUYfny5YwcOZI9e/bQpk0bXRdFRAB92em1EhMTr/fBz5w5wxtvvMGwYcO47770RoKKSH6mI3IvtHz5ch599FF69OhB5cqV2bJlC1OnTlWIi0i6FOReJCYmhpYtW9KoUSPi4+P5+uuvWblyJbVq1fJ0aSLixRTkXiAuLo4+ffpQpUoVfvrpJ8LDw9m9ezetW7dWH1xEsqQeuQclJiYyZcoUBg0axJkzZ+jWrRvDhg3j3nvv9XRpIuJDdETuIT/++CM1a9bkrbfeomrVqmzdupUpU6YoxEUkxxTkbrZv3z5atGhB48aNSUhIYP78+axYsYKaNWt6ujQR8VFqrbjJuXPnGDp0KOPHj8fPz4/Ro0fz7rvvUqRIEZdsT7P0iOQfCnIXS0xMZPLkyQwaNIhz587xt7/9jffff9+lLZTUWXpSJ3hInaUHUJiL5EFqrbjQ0qVLqVGjBm+//TbVq1dn69atTJo0yeV9cM3SI5K/KMhdYO/evTRv3pwmTZpw5coVFixYwPLly6lRo4Zbtq9ZekTyFwW5E509e5ZevXpRrVo11qxZQ0REBLt27aJly5ZuHQ+e0Ww8mqVHJG9SkDvBtWvX+OijjwgICGD8+PF069aNmJgY+vTp47IvMzOjWXpE8hd92ZkNmY0A+eGHH+jduzd79uyhYcOGjBs3jurVq3u0Xs3SI5K/KMizkNEIkKOH9hM5NZzvv/+eRx55hIULF/LSSy95zSn1mqVHJP9QkGfh5hEgSQkXiV32b94ZsZi7ihdn7Nix9OzZk8KFC6f7fI3nFhFXU5BnIXWkh01K5OK27zm/dhbJVy5RvGZTYpZMp3Tp0hk+V+O5RcQdFORZKFPCj/1b1nB2xVQSzx6l6EM1KdnwbzwcUCnTEIfMx3MryEXEWRTkmdi9ezcJ3w7l5PqV3FayDKVfGYTfX2pze+HbsjUCROO5RcQdFOTpOHPmDEOGDOGTTz6hePHivNFnCLtL1OW3+MQc9bnLlPAjNp3Q1nhuEXEmBXka165d4+OPPyYsLIzz58/To0cPwsLCKFWq1C2tr1+TCjf0yEHjuUXE+RTkgLWWyMhI+vTpQ3R0NM8//zzjxo2jatWquVqvxnOLiDvkiyDPbAjgrl276N27N0uXLqV8+fJ89913NGvWzGnjwTWeW0RcLc8HeUZDAC+cO8t/509i4sSJFC9enA8++IC33nqLQoUKebhiEZGcyfNBfvMQQJt0jRObFvJGxGy4lsCbb77JkCFDuPvuuz1YpYjIrcvzQX79hB5rSTiwiXM/fUri2ViKPvwoW777gsqVK3u4QhGR3MnzQV6mhB+HYvZwbsWnXP4litv+VJZ72gzhkceeUoiLSJ6Qp4P89OnT3Ll1Bse/mkmBIrdTsmF3itdqxu1Fi2gIoIjkGXkyyK9evcqECRMICwsjPj6eF9t35eQjL3HqaiENARSRPCdPBbm1lu+++44+ffoQExPDCy+8wNixY6lUqZKnSxMRcZk8M0PQzp07ady4MS1atOC2224jMjKSyMhIhbiI5Hk+H+SnTp3izTffpGbNmmzdupXx48ezfft2XnjhBU+XJiLiFrkKcmPMGGPMXmPMDmPMN8aYEs4qLCtXr15l7NixPPLII0ydOpV33nmHmJgYevbsqZN6RCRfyW2P/Eegv7U20RgTDvQHgnNf1h+lnmYfe+4SfsejOL/yM44f+YUXX3yRiIgIKlas6IrNioh4vVwFubV2aZpfNwBtcldO+lJPsz8fu59zK6Zw+fAOCpd6gEEfzSTs7U6u2KSIiM9wZo/8DeD7jO40xnQ3xmw2xmw+depUjlacepr9xajFXD1xiD8934P7/voRyy7en9uaRUR8XpZH5MaYZcB96dwVaq1d6HhMKJAIzMpoPdbaycBkgMDAQJuTIlNPsy/xdBdKPNOVgkXvuGG5iEh+lmWQW2sbZXa/MaYr0BxoaK3NUUBnV+pMOwX9iv9huYhIfpfbUStNgfeAFtbaS84p6Y/6NamAX6GCNyzTTDsiIilyO2rlI6AI8KNjIoYN1toeua7qJpppR0QkY7kdtfKIswrJimbaERFJn8+f2Skikt8pyEVEfJyCXETExynIRUR8nIJcRMTHGRedw5P5Ro05BRy+xaeXAk47sRxnUV05o7pyRnXljLfWBbmr7SFrbembF3okyHPDGLPZWhvo6TpuprpyRnXljOrKGW+tC1xTm1orIiI+TkEuIuLjfDHIJ3u6gAyorpxRXTmjunLGW+sCF9Tmcz1yERG5kS8ekYuISBoKchERH+eVQW6MedUYs8sYk2yMyXCYjjGmqTEm2hiz3xgTkmb5w8aYjY7lc40xhZ1U15+MMT8aY2Ic/5ZM5zHPGWO2pfm5bIxp5bhvujHmUJr7arqrLsfjktJse1Ga5Z7cXzWNMf9xvN47jDHt0tzn1P2V0fslzf1FHP/9+x37o1ya+/o7lkcbY5rkpo5bqKu3MWa3Y/8sN8Y8lOa+dF9TN9XV1RhzKs32/5bmvi6O1z3GGNPFzXX9M01N+4wxcWnuc+X++swYc9IY83MG9xtjzL8cde8wxjya5r7c7S9rrdf9AJWACsBKIDCDxxQEDgB/BgoD24HKjvu+BNo7bk8E3nRSXaOBEMftECA8i8f/CTgL3O74fTrQxgX7K1t1AfEZLPfY/gLKAwGO22WA40AJZ++vzN4vaR7zFjDRcbs9MNdxu7Lj8UWAhx3rKejGup5L8x56M7WuzF5TN9XVFfgonef+CTjo+Lek43ZJd9V10+PfAT5z9f5yrPtp4FHg5wzub0bKvMYGqAtsdNb+8sojcn9FwGMAAAQkSURBVGvtHmttdBYPexzYb609aK29CswBWhpjDNAA+MrxuBlAKyeV1tKxvuyutw3wvXXh7EkOOa3rOk/vL2vtPmttjOP2MeAk8Icz15wg3fdLJvV+BTR07J+WwBxr7RVr7SFgv2N9bqnLWvtTmvfQBqCsk7adq7oy0QT40Vp71lp7DvgRaOqhujoAs5207UxZa1eTcuCWkZbA5zbFBqCEMeZ+nLC/vDLIs8kfOJLm96OOZXcDcdbaxJuWO8O91trjjtu/Afdm8fj2/PFNNNzxZ9U/jTFF3FxXUWPMZmPMhtR2D160v4wxj5NylHUgzWJn7a+M3i/pPsaxP86Tsn+y81xX1pVWN1KO6lKl95q6s65XHK/PV8aYB3L4XFfWhaMF9TCwIs1iV+2v7Mio9lzvr9xO9XbLjDHLgPvSuSvUWrvQ3fWkyqyutL9Ya60xJsOxm45P2mrAkjSL+5MSaIVJGUsaDLzvxroestbGGmP+DKwwxuwkJaxumZP31xdAF2ttsmPxLe+vvMgY8xoQCDyTZvEfXlNr7YH01+B03wKzrbVXjDH/IOWvmQZu2nZ2tAe+stYmpVnmyf3lMh4Lcmtto1yuIhZ4IM3vZR3LzpDyJ8ttjqOq1OW5rssYc8IYc7+19rgjeE5msqq2wDfW2mtp1p16dHrFGDMN6OvOuqy1sY5/DxpjVgK1gK/x8P4yxtwJLCblQ3xDmnXf8v5KR0bvl/Qec9QYcxtwFynvp+w815V1YYxpRMqH4zPW2iupyzN4TZ0RTFnWZa09k+bXqaR8J5L63Gdveu5KJ9SUrbrSaA+8nXaBC/dXdmRUe673ly+3VjYBASZlxEVhUl60RTbl24OfSOlPA3QBnHWEv8ixvuys9w+9OUeYpfalWwHpfrvtirqMMSVTWxPGmFJAfWC3p/eX47X7hpTe4Vc33efM/ZXu+yWTetsAKxz7ZxHQ3qSMankYCAD+m4taclSXMaYWMAloYa09mWZ5uq+pG+u6P82vLYA9jttLgMaO+koCjbnxL1OX1uWorSIpXxz+J80yV+6v7FgEdHaMXqkLnHccrOR+f7nqG9zc/AAvk9InugKcAJY4lpcBItM8rhmwj5RP1NA0y/9Myv9o+4F5QBEn1XU3sByIAZYBf3IsDwSmpnlcOVI+ZQvc9PwVwE5SAmkmcIe76gLqOba93fFvN2/YX8BrwDVgW5qfmq7YX+m9X0hp1bRw3C7q+O/f79gff07z3FDH86KBF5z8fs+qrmWO/w9S98+irF5TN9U1Etjl2P5PQMU0z33DsR/3A391Z12O34cAo256nqv312xSRl1dIyW/ugE9gB6O+w0wwVH3TtKMyMvt/tIp+iIiPs6XWysiIoKCXETE5ynIRUR8nIJcRMTHKchFRHycglxExMcpyEVEfNz/AVoJx2mrMSnYAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter([t[0] for t in test_data],[t[1] for t in test_data])\n",
    "plot_function(lambda x: 2*x,-1,1,c='k')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the drawing routine I used to illustrate the absolute value cost function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_cost(h,points):\n",
    "    xs = [t[0] for t in points]\n",
    "    ys = [t[1] for t in points]\n",
    "    plt.scatter(xs,ys)\n",
    "    plot_function(h,min(xs),max(xs),c='k')\n",
    "    for (x,y) in points:\n",
    "        plt.plot([x,x],[y,h(x)],c='r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_cost(lambda x: 2*x, test_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sum_error(f,data):\n",
    "    errors = [abs(f(x) - y) for (x,y) in data]\n",
    "    return sum(errors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x): \n",
    "    return 2*x\n",
    "\n",
    "def g(x): \n",
    "    return 1-x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.021727176394801"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum_error(f,test_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "38.47711311130152"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum_error(g,test_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 14.1.2 Summing the squares of the errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sum_squared_error(f,data):\n",
    "    squared_errors = [(f(x) - y)**2 for (x,y) in data]\n",
    "    return sum(squared_errors)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "here's a function to picture the sum_squared_error for a line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_square_cost(h,points):\n",
    "    xs = [t[0] for t in points]\n",
    "    ys = [t[1] for t in points]\n",
    "    plt.scatter(xs,ys)\n",
    "    plot_function(h,min(xs),max(xs),c='k')\n",
    "    for (x,y) in points:\n",
    "        e = abs(y - h(x))\n",
    "        plt.plot([x,x],[y,h(x)],c='r')\n",
    "        plt.fill([x,x,x+e,x+e],[h(x),y,y,h(x)],c='r',alpha=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_square_cost(lambda x: 2*x, test_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.105175107540148"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum_squared_error(f,test_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "97.1078879283203"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "97.1078879283203"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 14.1.3 Calculating cost for car price functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_mileage_price(cars):\n",
    "    prices = [c.price for c in cars]\n",
    "    mileages = [c.mileage for c in cars]\n",
    "    plt.scatter(mileages, prices, alpha=0.5)\n",
    "    plt.ylabel(\"Price ($)\",fontsize=16)\n",
    "    plt.xlabel(\"Odometer (mi)\",fontsize=16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def p1(x):\n",
    "    return 25000 - 0.2 * x\n",
    "\n",
    "def p2(x):\n",
    "    return 25000 - 0.1 * x\n",
    "\n",
    "def p3(x):\n",
    "    return 22500 - 0.1 * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_mileage_price(priuses)\n",
    "plot_function(p1,0,125000,c='k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_mileage_price(priuses)\n",
    "plot_function(p2,0,250000,c='k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_mileage_price(priuses)\n",
    "plot_function(p3,0,225000,c='k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "prius_mileage_price = [(p.mileage, p.price) for p in priuses]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "88782506640.23999"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum_squared_error(p1, prius_mileage_price)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "34723507681.55999"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum_squared_error(p2, prius_mileage_price)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22997230681.560013"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum_squared_error(p3, prius_mileage_price)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 14.1.4 Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Create a set of data points lying on a line and demonstrate that the `sum_error` and `sum_squared_error` cost functions both return exactly zero for the appropriate linear function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def line(x):\n",
    "    return 3*x-2\n",
    "points = [(x,line(x)) for x in range(0,10)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum_error(line,points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum_squared_error(line,points)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Calculate the value of the cost for the two linear functions $x + 0.5$ and $2x - 1$.  Which one produces a lower sum squared error relative to the `test_data` and what does that say about the quality of the fits?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "23.1942461283472"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum_squared_error(lambda x:2*x-1,test_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16.607900877665685"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum_squared_error(lambda x:x+0.5,test_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Find a linear function `p4` that fits the data even better than `p1`, `p2`, or `p3`.  Demonstrate that it is a better fit by showing the cost function is lower than for `p1`, `p2`, or `p3`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "def p4(x):\n",
    "    return 20000 - 0.1 * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "18958453681.56001"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum_squared_error(p4, prius_mileage_price)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 14.2 Exploring spaces of functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 14.2.1 Picturing cost for lines through the origin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def test_data_coefficient_cost(a):\n",
    "    def f(x):\n",
    "        return a * x\n",
    "    return sum_squared_error(f,test_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plots from the chapter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'a')"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "some_slopes = [-1,0,1,2,3]\n",
    "plt.scatter(some_slopes,[test_data_coefficient_cost(a) for a in some_slopes])\n",
    "plt.ylabel(\"cost\", fontsize=16)\n",
    "plt.xlabel(\"a\", fontsize=16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'x')"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter([t[0] for t in test_data],[t[1] for t in test_data])\n",
    "for a in some_slopes:\n",
    "    plot_function(lambda x: a*x, -1, 1, c='k')\n",
    "plt.ylabel(\"y\", fontsize=16)\n",
    "plt.xlabel(\"x\", fontsize=16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'a')"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_function(test_data_coefficient_cost, -5, 5)\n",
    "plt.ylabel(\"cost\", fontsize=16)\n",
    "plt.xlabel(\"a\", fontsize=16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 14.2.2 The space of all linear functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "def coefficient_cost(a,b):\n",
    "    def p(x):\n",
    "        return a * x + b\n",
    "    return sum_squared_error(p,prius_mileage_price)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "def coefficient_cost(a,b):\n",
    "    def p(x):\n",
    "        return a * x + b\n",
    "    return sum_squared_error(p,prius_mileage_price)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plots from the chapter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_mileage_price(priuses)\n",
    "plot_function(lambda x: 25000 - 0.20*x,0,125000,c='k')\n",
    "plot_function(lambda x: 5000 + 0.05*x,0,350000,c='k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'a')"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 504x504 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "scalar_field_heatmap(coefficient_cost,-0.5,0.5,-50000,50000)\n",
    "plt.ylabel(\"b\",fontsize=16)\n",
    "plt.xlabel(\"a\",fontsize=16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 14.2.3 Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 14.3 Finding the line of best fit using gradient descent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 14.3.1 Rescaling the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "def scaled_cost_function(c,d):\n",
    "    return coefficient_cost(0.5*c,50000*d)/1e13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "mileages = [p.mileage for p in priuses]\n",
    "prices = [p.price for p in priuses]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "def scaled_cost_function(c,d):\n",
    "    return coefficient_cost(0.5*c,50000*d)/1e13"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 14.3.2 Finding and plotting the line of best fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "c,d = gradient_descent(scaled_cost_function,0,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.12111901781185214, 0.314954228880389)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(c,d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.06055950890592607, 15747.71144401945)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = 0.5*c\n",
    "b = 50000*d\n",
    "(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_mileage_price(priuses)\n",
    "\n",
    "def p(x):\n",
    "    return a*x + b\n",
    "\n",
    "plot_function(p,0,250000,c='k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14536218169.403488"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coefficient_cost(a,b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 14.3.3 Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Use gradient descent to find the linear function that best fits the `test_data`.  Your resulting function should be close to $2x + 0$ but not exactly, because the data was randomly generated around that line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "def test_data_linear_cost(a,b):\n",
    "    def f(x):\n",
    "        return a*x+b\n",
    "    return sum_squared_error(f,test_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 504x504 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "scalar_field_heatmap(test_data_linear_cost,-0,4,-2,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.103718204728344, 0.0021207385859157535)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gradient_descent(test_data_linear_cost,1,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 14.4 Fitting a nonlinear function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 14.4.1 Understanding the behavior of exponential functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import exp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_mileage_price(priuses)\n",
    "plt.ylim(-5000,35000)\n",
    "plt.xlim(0,375000)\n",
    "plot_function(lambda x:0, -50000, 400000, c='gray')\n",
    "q,r = (16133.220556990309, -5.951793936498175e-06)\n",
    "plot_function(lambda x: q*exp(r*x),0,375000,c='k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_mileage_price(priuses)\n",
    "plt.ylim(-5000,35000)\n",
    "plt.xlim(0,375000)\n",
    "plot_function(lambda x:0, -50000, 400000, c='gray')\n",
    "\n",
    "plot_function(lambda x: a*x + b,0,375000,c='k')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 14.4.2 Finding the exponential function of best fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "def exp_coefficient_cost(q,r):\n",
    "    def f(x):\n",
    "        return q*exp(r*x) #<1>\n",
    "    return sum_squared_error(f,prius_mileage_price)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 504x504 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def scaled_exp_coefficient_cost(s,t):\n",
    "    return exp_coefficient_cost(30000*s,1e-4*t) / 1e11\n",
    "\n",
    "scalar_field_heatmap(scaled_exp_coefficient_cost,0,1,-1,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.6235404892898214, -0.07686877731180546)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s,t = gradient_descent(scaled_exp_coefficient_cost,0,0)\n",
    "(s,t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(18706.214678694643, -7.686877731180546e-06)"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q,r = 30000*s,1e-4*t\n",
    "(q,r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_mileage_price(priuses)\n",
    "q,r = (16133.220556990309, -5.951793936498175e-06)\n",
    "plot_function(lambda x: q*exp(r*x),0,375000,c='k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14071654468.280859"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exp_coefficient_cost(q,r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 14.4.3 Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Confirm, by choosing a sample value of $r$, that $e^{-rx}$ decreases by a factor of $e$ every time $x$ increases by $1/r$ units."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "def test(x):\n",
    "    return exp(-3*x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.36787944117144233, 0.36787944117144233)"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test(1/3), test(0)/e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.1353352832366127, 0.1353352832366127)"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(0.1353352832366127, 0.1353352832366127)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.049787068367863944, 0.04978706836786395)"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(0.049787068367863944, 0.04978706836786395)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** According to the exponential function of best fit, what percent of the value of a prius is lost every 10,000 miles?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9422186306357088"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exp(r * 10000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Asserting that the retail price (the price at zero miles) is $\\$25,000$ what is the exponential function that best fits the data?  In other words, fixing $q = 25,000$, what is the value of $r$ yielding the best fit for $qe^{rx}$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "def exponential_cost2(r):\n",
    "    def f(x):\n",
    "        return 25000 * exp(r*x)\n",
    "    return sum_squared_error(f,prius_mileage_price)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_function(exponential_cost2,-1e-4,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(16157457680.500858, 16156919168.114105, 16161508051.813206)"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# note that r = -1.12e-5 yields a smaller cost function than some values around it.\n",
    "exponential_cost2(-1.11e-5), exponential_cost2(-1.12e-5), exponential_cost2(-1.13e-5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_mileage_price(priuses)\n",
    "plot_function(lambda x: 25000 * exp(-1.12e-5 * x), 0, 350000, c='k')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
